Properties

Label 177.10.a.a.1.21
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $1$
Dimension $21$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(91.1613430010\)
Analytic rank: \(1\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.21
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+39.7755 q^{2} +81.0000 q^{3} +1070.09 q^{4} -1731.07 q^{5} +3221.81 q^{6} -3884.78 q^{7} +22198.2 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q+39.7755 q^{2} +81.0000 q^{3} +1070.09 q^{4} -1731.07 q^{5} +3221.81 q^{6} -3884.78 q^{7} +22198.2 q^{8} +6561.00 q^{9} -68854.3 q^{10} +56874.0 q^{11} +86677.2 q^{12} -109727. q^{13} -154519. q^{14} -140217. q^{15} +335060. q^{16} -653147. q^{17} +260967. q^{18} -175919. q^{19} -1.85240e6 q^{20} -314668. q^{21} +2.26219e6 q^{22} -1.42571e6 q^{23} +1.79806e6 q^{24} +1.04349e6 q^{25} -4.36446e6 q^{26} +531441. q^{27} -4.15706e6 q^{28} +7.18211e6 q^{29} -5.57720e6 q^{30} -6.64880e6 q^{31} +1.96168e6 q^{32} +4.60680e6 q^{33} -2.59792e7 q^{34} +6.72485e6 q^{35} +7.02085e6 q^{36} +8.37955e6 q^{37} -6.99726e6 q^{38} -8.88792e6 q^{39} -3.84268e7 q^{40} +1.93751e7 q^{41} -1.25161e7 q^{42} -2.28822e7 q^{43} +6.08602e7 q^{44} -1.13576e7 q^{45} -5.67085e7 q^{46} -5.30532e7 q^{47} +2.71399e7 q^{48} -2.52621e7 q^{49} +4.15054e7 q^{50} -5.29049e7 q^{51} -1.17418e8 q^{52} -5.99352e7 q^{53} +2.11383e7 q^{54} -9.84532e7 q^{55} -8.62354e7 q^{56} -1.42494e7 q^{57} +2.85672e8 q^{58} +1.21174e7 q^{59} -1.50045e8 q^{60} +1.37319e8 q^{61} -2.64459e8 q^{62} -2.54881e7 q^{63} -9.35241e7 q^{64} +1.89946e8 q^{65} +1.83238e8 q^{66} -2.40791e8 q^{67} -6.98925e8 q^{68} -1.15483e8 q^{69} +2.67484e8 q^{70} +2.40527e8 q^{71} +1.45643e8 q^{72} +1.45532e8 q^{73} +3.33301e8 q^{74} +8.45230e7 q^{75} -1.88249e8 q^{76} -2.20943e8 q^{77} -3.53521e8 q^{78} -4.07178e8 q^{79} -5.80014e8 q^{80} +4.30467e7 q^{81} +7.70653e8 q^{82} +3.98650e8 q^{83} -3.36722e8 q^{84} +1.13065e9 q^{85} -9.10149e8 q^{86} +5.81751e8 q^{87} +1.26250e9 q^{88} -2.64491e6 q^{89} -4.51753e8 q^{90} +4.26267e8 q^{91} -1.52564e9 q^{92} -5.38553e8 q^{93} -2.11022e9 q^{94} +3.04529e8 q^{95} +1.58896e8 q^{96} +1.02578e9 q^{97} -1.00481e9 q^{98} +3.73151e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} + O(q^{10}) \) \( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} - 54663q^{10} - 151769q^{11} + 421686q^{12} - 153611q^{13} - 286771q^{14} - 240084q^{15} + 805530q^{16} - 723621q^{17} - 433026q^{18} - 549388q^{19} - 527311q^{20} - 2492775q^{21} + 2973158q^{22} + 169962q^{23} - 1994301q^{24} + 8035779q^{25} - 2337392q^{26} + 11160261q^{27} - 22659054q^{28} - 16845442q^{29} - 4427703q^{30} - 19307976q^{31} - 44923568q^{32} - 12293289q^{33} - 35547496q^{34} - 34882596q^{35} + 34156566q^{36} - 41561129q^{37} - 52335371q^{38} - 12442491q^{39} - 125735038q^{40} - 68169291q^{41} - 23228451q^{42} - 25719587q^{43} - 126277032q^{44} - 19446804q^{45} - 292814271q^{46} - 174095332q^{47} + 65247930q^{48} + 7479350q^{49} - 227877439q^{50} - 58613301q^{51} - 232397708q^{52} - 228390500q^{53} - 35075106q^{54} - 29426208q^{55} + 326778474q^{56} - 44500428q^{57} + 480343762q^{58} + 254464581q^{59} - 42712191q^{60} - 183928964q^{61} - 21753862q^{62} - 201914775q^{63} + 310571245q^{64} + 5308466q^{65} + 240825798q^{66} - 82724114q^{67} - 138336205q^{68} + 13766922q^{69} + 1030274876q^{70} - 404721965q^{71} - 161538381q^{72} + 154162574q^{73} + 36352054q^{74} + 650898099q^{75} + 1068940636q^{76} - 448535481q^{77} - 189328752q^{78} + 272529635q^{79} - 345587859q^{80} + 903981141q^{81} - 38412637q^{82} + 432518643q^{83} - 1835383374q^{84} - 126211490q^{85} - 3699273072q^{86} - 1364480802q^{87} + 170111045q^{88} - 1255621070q^{89} - 358643943q^{90} + 1448885849q^{91} + 1568933320q^{92} - 1563946056q^{93} - 1908445164q^{94} - 2896546490q^{95} - 3638809008q^{96} + 1007235486q^{97} - 9506868248q^{98} - 995756409q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 39.7755 1.75784 0.878922 0.476965i \(-0.158263\pi\)
0.878922 + 0.476965i \(0.158263\pi\)
\(3\) 81.0000 0.577350
\(4\) 1070.09 2.09002
\(5\) −1731.07 −1.23866 −0.619328 0.785132i \(-0.712595\pi\)
−0.619328 + 0.785132i \(0.712595\pi\)
\(6\) 3221.81 1.01489
\(7\) −3884.78 −0.611541 −0.305771 0.952105i \(-0.598914\pi\)
−0.305771 + 0.952105i \(0.598914\pi\)
\(8\) 22198.2 1.91608
\(9\) 6561.00 0.333333
\(10\) −68854.3 −2.17736
\(11\) 56874.0 1.17124 0.585621 0.810585i \(-0.300851\pi\)
0.585621 + 0.810585i \(0.300851\pi\)
\(12\) 86677.2 1.20667
\(13\) −109727. −1.06554 −0.532770 0.846260i \(-0.678849\pi\)
−0.532770 + 0.846260i \(0.678849\pi\)
\(14\) −154519. −1.07499
\(15\) −140217. −0.715138
\(16\) 335060. 1.27815
\(17\) −653147. −1.89667 −0.948333 0.317276i \(-0.897232\pi\)
−0.948333 + 0.317276i \(0.897232\pi\)
\(18\) 260967. 0.585948
\(19\) −175919. −0.309686 −0.154843 0.987939i \(-0.549487\pi\)
−0.154843 + 0.987939i \(0.549487\pi\)
\(20\) −1.85240e6 −2.58881
\(21\) −314668. −0.353074
\(22\) 2.26219e6 2.05886
\(23\) −1.42571e6 −1.06233 −0.531163 0.847270i \(-0.678245\pi\)
−0.531163 + 0.847270i \(0.678245\pi\)
\(24\) 1.79806e6 1.10625
\(25\) 1.04349e6 0.534269
\(26\) −4.36446e6 −1.87305
\(27\) 531441. 0.192450
\(28\) −4.15706e6 −1.27813
\(29\) 7.18211e6 1.88565 0.942825 0.333288i \(-0.108158\pi\)
0.942825 + 0.333288i \(0.108158\pi\)
\(30\) −5.57720e6 −1.25710
\(31\) −6.64880e6 −1.29305 −0.646526 0.762892i \(-0.723779\pi\)
−0.646526 + 0.762892i \(0.723779\pi\)
\(32\) 1.96168e6 0.330714
\(33\) 4.60680e6 0.676217
\(34\) −2.59792e7 −3.33404
\(35\) 6.72485e6 0.757489
\(36\) 7.02085e6 0.696672
\(37\) 8.37955e6 0.735043 0.367522 0.930015i \(-0.380206\pi\)
0.367522 + 0.930015i \(0.380206\pi\)
\(38\) −6.99726e6 −0.544380
\(39\) −8.88792e6 −0.615190
\(40\) −3.84268e7 −2.37336
\(41\) 1.93751e7 1.07082 0.535410 0.844592i \(-0.320157\pi\)
0.535410 + 0.844592i \(0.320157\pi\)
\(42\) −1.25161e7 −0.620648
\(43\) −2.28822e7 −1.02068 −0.510339 0.859973i \(-0.670480\pi\)
−0.510339 + 0.859973i \(0.670480\pi\)
\(44\) 6.08602e7 2.44792
\(45\) −1.13576e7 −0.412885
\(46\) −5.67085e7 −1.86740
\(47\) −5.30532e7 −1.58588 −0.792942 0.609297i \(-0.791452\pi\)
−0.792942 + 0.609297i \(0.791452\pi\)
\(48\) 2.71399e7 0.737942
\(49\) −2.52621e7 −0.626017
\(50\) 4.15054e7 0.939161
\(51\) −5.29049e7 −1.09504
\(52\) −1.17418e8 −2.22700
\(53\) −5.99352e7 −1.04338 −0.521688 0.853136i \(-0.674698\pi\)
−0.521688 + 0.853136i \(0.674698\pi\)
\(54\) 2.11383e7 0.338297
\(55\) −9.84532e7 −1.45077
\(56\) −8.62354e7 −1.17176
\(57\) −1.42494e7 −0.178797
\(58\) 2.85672e8 3.31468
\(59\) 1.21174e7 0.130189
\(60\) −1.50045e8 −1.49465
\(61\) 1.37319e8 1.26983 0.634916 0.772581i \(-0.281035\pi\)
0.634916 + 0.772581i \(0.281035\pi\)
\(62\) −2.64459e8 −2.27298
\(63\) −2.54881e7 −0.203847
\(64\) −9.35241e7 −0.696809
\(65\) 1.89946e8 1.31984
\(66\) 1.83238e8 1.18868
\(67\) −2.40791e8 −1.45983 −0.729917 0.683536i \(-0.760441\pi\)
−0.729917 + 0.683536i \(0.760441\pi\)
\(68\) −6.98925e8 −3.96406
\(69\) −1.15483e8 −0.613334
\(70\) 2.67484e8 1.33155
\(71\) 2.40527e8 1.12332 0.561658 0.827369i \(-0.310164\pi\)
0.561658 + 0.827369i \(0.310164\pi\)
\(72\) 1.45643e8 0.638693
\(73\) 1.45532e8 0.599798 0.299899 0.953971i \(-0.403047\pi\)
0.299899 + 0.953971i \(0.403047\pi\)
\(74\) 3.33301e8 1.29209
\(75\) 8.45230e7 0.308460
\(76\) −1.88249e8 −0.647249
\(77\) −2.20943e8 −0.716263
\(78\) −3.53521e8 −1.08141
\(79\) −4.07178e8 −1.17615 −0.588075 0.808806i \(-0.700114\pi\)
−0.588075 + 0.808806i \(0.700114\pi\)
\(80\) −5.80014e8 −1.58319
\(81\) 4.30467e7 0.111111
\(82\) 7.70653e8 1.88233
\(83\) 3.98650e8 0.922019 0.461009 0.887395i \(-0.347487\pi\)
0.461009 + 0.887395i \(0.347487\pi\)
\(84\) −3.36722e8 −0.737929
\(85\) 1.13065e9 2.34932
\(86\) −9.10149e8 −1.79419
\(87\) 5.81751e8 1.08868
\(88\) 1.26250e9 2.24419
\(89\) −2.64491e6 −0.00446844 −0.00223422 0.999998i \(-0.500711\pi\)
−0.00223422 + 0.999998i \(0.500711\pi\)
\(90\) −4.51753e8 −0.725788
\(91\) 4.26267e8 0.651622
\(92\) −1.52564e9 −2.22028
\(93\) −5.38553e8 −0.746543
\(94\) −2.11022e9 −2.78774
\(95\) 3.04529e8 0.383594
\(96\) 1.58896e8 0.190938
\(97\) 1.02578e9 1.17647 0.588237 0.808689i \(-0.299822\pi\)
0.588237 + 0.808689i \(0.299822\pi\)
\(98\) −1.00481e9 −1.10044
\(99\) 3.73151e8 0.390414
\(100\) 1.11663e9 1.11663
\(101\) −1.75741e9 −1.68046 −0.840228 0.542233i \(-0.817579\pi\)
−0.840228 + 0.542233i \(0.817579\pi\)
\(102\) −2.10432e9 −1.92491
\(103\) −1.93271e9 −1.69199 −0.845996 0.533189i \(-0.820993\pi\)
−0.845996 + 0.533189i \(0.820993\pi\)
\(104\) −2.43575e9 −2.04166
\(105\) 5.44713e8 0.437337
\(106\) −2.38395e9 −1.83409
\(107\) −4.90766e8 −0.361949 −0.180975 0.983488i \(-0.557925\pi\)
−0.180975 + 0.983488i \(0.557925\pi\)
\(108\) 5.68689e8 0.402224
\(109\) 1.67260e9 1.13494 0.567470 0.823394i \(-0.307922\pi\)
0.567470 + 0.823394i \(0.307922\pi\)
\(110\) −3.91602e9 −2.55022
\(111\) 6.78744e8 0.424378
\(112\) −1.30164e9 −0.781643
\(113\) −1.07595e9 −0.620780 −0.310390 0.950609i \(-0.600460\pi\)
−0.310390 + 0.950609i \(0.600460\pi\)
\(114\) −5.66778e8 −0.314298
\(115\) 2.46802e9 1.31586
\(116\) 7.68549e9 3.94104
\(117\) −7.19921e8 −0.355180
\(118\) 4.81974e8 0.228852
\(119\) 2.53734e9 1.15989
\(120\) −3.11257e9 −1.37026
\(121\) 8.76708e8 0.371810
\(122\) 5.46193e9 2.23217
\(123\) 1.56938e9 0.618238
\(124\) −7.11480e9 −2.70250
\(125\) 1.57464e9 0.576881
\(126\) −1.01380e9 −0.358331
\(127\) 4.53115e9 1.54558 0.772790 0.634661i \(-0.218860\pi\)
0.772790 + 0.634661i \(0.218860\pi\)
\(128\) −4.72434e9 −1.55560
\(129\) −1.85346e9 −0.589289
\(130\) 7.55520e9 2.32007
\(131\) 1.76844e9 0.524651 0.262325 0.964979i \(-0.415511\pi\)
0.262325 + 0.964979i \(0.415511\pi\)
\(132\) 4.92968e9 1.41331
\(133\) 6.83407e8 0.189386
\(134\) −9.57757e9 −2.56616
\(135\) −9.19964e8 −0.238379
\(136\) −1.44987e10 −3.63416
\(137\) 5.62271e9 1.36365 0.681825 0.731515i \(-0.261186\pi\)
0.681825 + 0.731515i \(0.261186\pi\)
\(138\) −4.59339e9 −1.07815
\(139\) 2.41920e9 0.549673 0.274837 0.961491i \(-0.411376\pi\)
0.274837 + 0.961491i \(0.411376\pi\)
\(140\) 7.19619e9 1.58317
\(141\) −4.29731e9 −0.915610
\(142\) 9.56709e9 1.97462
\(143\) −6.24064e9 −1.24801
\(144\) 2.19833e9 0.426051
\(145\) −1.24328e10 −2.33567
\(146\) 5.78859e9 1.05435
\(147\) −2.04623e9 −0.361431
\(148\) 8.96686e9 1.53625
\(149\) 3.82633e9 0.635981 0.317991 0.948094i \(-0.396992\pi\)
0.317991 + 0.948094i \(0.396992\pi\)
\(150\) 3.36194e9 0.542225
\(151\) 1.04501e10 1.63577 0.817885 0.575382i \(-0.195147\pi\)
0.817885 + 0.575382i \(0.195147\pi\)
\(152\) −3.90509e9 −0.593383
\(153\) −4.28530e9 −0.632222
\(154\) −8.78813e9 −1.25908
\(155\) 1.15096e10 1.60165
\(156\) −9.51086e9 −1.28576
\(157\) −9.41439e9 −1.23664 −0.618321 0.785926i \(-0.712187\pi\)
−0.618321 + 0.785926i \(0.712187\pi\)
\(158\) −1.61957e10 −2.06749
\(159\) −4.85475e9 −0.602393
\(160\) −3.39581e9 −0.409641
\(161\) 5.53860e9 0.649656
\(162\) 1.71220e9 0.195316
\(163\) 7.04946e9 0.782189 0.391094 0.920351i \(-0.372097\pi\)
0.391094 + 0.920351i \(0.372097\pi\)
\(164\) 2.07331e10 2.23803
\(165\) −7.97471e9 −0.837601
\(166\) 1.58565e10 1.62077
\(167\) −2.24805e9 −0.223657 −0.111828 0.993728i \(-0.535671\pi\)
−0.111828 + 0.993728i \(0.535671\pi\)
\(168\) −6.98506e9 −0.676517
\(169\) 1.43560e9 0.135377
\(170\) 4.49720e10 4.12973
\(171\) −1.15420e9 −0.103229
\(172\) −2.44859e10 −2.13324
\(173\) −1.65130e9 −0.140159 −0.0700793 0.997541i \(-0.522325\pi\)
−0.0700793 + 0.997541i \(0.522325\pi\)
\(174\) 2.31394e10 1.91373
\(175\) −4.05375e9 −0.326727
\(176\) 1.90562e10 1.49703
\(177\) 9.81506e8 0.0751646
\(178\) −1.05202e8 −0.00785481
\(179\) 3.11437e9 0.226742 0.113371 0.993553i \(-0.463835\pi\)
0.113371 + 0.993553i \(0.463835\pi\)
\(180\) −1.21536e10 −0.862937
\(181\) −1.29740e10 −0.898508 −0.449254 0.893404i \(-0.648310\pi\)
−0.449254 + 0.893404i \(0.648310\pi\)
\(182\) 1.69550e10 1.14545
\(183\) 1.11228e10 0.733138
\(184\) −3.16484e10 −2.03550
\(185\) −1.45056e10 −0.910466
\(186\) −2.14212e10 −1.31231
\(187\) −3.71471e10 −2.22146
\(188\) −5.67716e10 −3.31452
\(189\) −2.06453e9 −0.117691
\(190\) 1.21128e10 0.674299
\(191\) 1.37305e10 0.746509 0.373255 0.927729i \(-0.378242\pi\)
0.373255 + 0.927729i \(0.378242\pi\)
\(192\) −7.57545e9 −0.402303
\(193\) 3.59947e10 1.86737 0.933685 0.358095i \(-0.116574\pi\)
0.933685 + 0.358095i \(0.116574\pi\)
\(194\) 4.08010e10 2.06806
\(195\) 1.53856e10 0.762009
\(196\) −2.70326e10 −1.30839
\(197\) −3.11152e10 −1.47189 −0.735944 0.677042i \(-0.763262\pi\)
−0.735944 + 0.677042i \(0.763262\pi\)
\(198\) 1.48422e10 0.686288
\(199\) −2.66121e10 −1.20293 −0.601466 0.798898i \(-0.705416\pi\)
−0.601466 + 0.798898i \(0.705416\pi\)
\(200\) 2.31637e10 1.02370
\(201\) −1.95041e10 −0.842835
\(202\) −6.99019e10 −2.95398
\(203\) −2.79010e10 −1.15315
\(204\) −5.66130e10 −2.28865
\(205\) −3.35397e10 −1.32638
\(206\) −7.68743e10 −2.97426
\(207\) −9.35412e9 −0.354108
\(208\) −3.67653e10 −1.36192
\(209\) −1.00052e10 −0.362717
\(210\) 2.16662e10 0.768770
\(211\) −2.16068e10 −0.750445 −0.375223 0.926935i \(-0.622434\pi\)
−0.375223 + 0.926935i \(0.622434\pi\)
\(212\) −6.41360e10 −2.18067
\(213\) 1.94827e10 0.648547
\(214\) −1.95205e10 −0.636250
\(215\) 3.96107e10 1.26427
\(216\) 1.17971e10 0.368750
\(217\) 2.58292e10 0.790754
\(218\) 6.65284e10 1.99505
\(219\) 1.17881e10 0.346293
\(220\) −1.05354e11 −3.03213
\(221\) 7.16682e10 2.02098
\(222\) 2.69974e10 0.745990
\(223\) 1.86803e10 0.505839 0.252919 0.967487i \(-0.418609\pi\)
0.252919 + 0.967487i \(0.418609\pi\)
\(224\) −7.62069e9 −0.202245
\(225\) 6.84636e9 0.178090
\(226\) −4.27963e10 −1.09123
\(227\) 3.29772e10 0.824324 0.412162 0.911111i \(-0.364774\pi\)
0.412162 + 0.911111i \(0.364774\pi\)
\(228\) −1.52482e10 −0.373689
\(229\) −8.98402e9 −0.215879 −0.107940 0.994157i \(-0.534425\pi\)
−0.107940 + 0.994157i \(0.534425\pi\)
\(230\) 9.81666e10 2.31307
\(231\) −1.78964e10 −0.413535
\(232\) 1.59430e11 3.61306
\(233\) −1.36044e10 −0.302396 −0.151198 0.988503i \(-0.548313\pi\)
−0.151198 + 0.988503i \(0.548313\pi\)
\(234\) −2.86352e10 −0.624351
\(235\) 9.18391e10 1.96436
\(236\) 1.29666e10 0.272097
\(237\) −3.29814e10 −0.679051
\(238\) 1.00924e11 2.03891
\(239\) 1.11203e10 0.220458 0.110229 0.993906i \(-0.464842\pi\)
0.110229 + 0.993906i \(0.464842\pi\)
\(240\) −4.69811e10 −0.914056
\(241\) 3.53983e10 0.675936 0.337968 0.941158i \(-0.390260\pi\)
0.337968 + 0.941158i \(0.390260\pi\)
\(242\) 3.48715e10 0.653584
\(243\) 3.48678e9 0.0641500
\(244\) 1.46944e11 2.65397
\(245\) 4.37305e10 0.775420
\(246\) 6.24229e10 1.08677
\(247\) 1.93031e10 0.329983
\(248\) −1.47592e11 −2.47759
\(249\) 3.22906e10 0.532328
\(250\) 6.26321e10 1.01407
\(251\) −1.14639e11 −1.82305 −0.911525 0.411244i \(-0.865094\pi\)
−0.911525 + 0.411244i \(0.865094\pi\)
\(252\) −2.72745e10 −0.426044
\(253\) −8.10862e10 −1.24424
\(254\) 1.80229e11 2.71689
\(255\) 9.15824e10 1.35638
\(256\) −1.40029e11 −2.03769
\(257\) 5.77628e10 0.825942 0.412971 0.910744i \(-0.364491\pi\)
0.412971 + 0.910744i \(0.364491\pi\)
\(258\) −7.37221e10 −1.03588
\(259\) −3.25528e10 −0.449509
\(260\) 2.03259e11 2.75848
\(261\) 4.71218e10 0.628550
\(262\) 7.03407e10 0.922255
\(263\) −2.65909e10 −0.342714 −0.171357 0.985209i \(-0.554815\pi\)
−0.171357 + 0.985209i \(0.554815\pi\)
\(264\) 1.02263e11 1.29569
\(265\) 1.03752e11 1.29238
\(266\) 2.71828e10 0.332911
\(267\) −2.14238e8 −0.00257985
\(268\) −2.57667e11 −3.05108
\(269\) −3.56944e10 −0.415638 −0.207819 0.978167i \(-0.566637\pi\)
−0.207819 + 0.978167i \(0.566637\pi\)
\(270\) −3.65920e10 −0.419034
\(271\) 9.29397e9 0.104674 0.0523371 0.998629i \(-0.483333\pi\)
0.0523371 + 0.998629i \(0.483333\pi\)
\(272\) −2.18844e11 −2.42423
\(273\) 3.45277e10 0.376214
\(274\) 2.23646e11 2.39709
\(275\) 5.93477e10 0.625758
\(276\) −1.23577e11 −1.28188
\(277\) −5.13710e10 −0.524275 −0.262137 0.965031i \(-0.584427\pi\)
−0.262137 + 0.965031i \(0.584427\pi\)
\(278\) 9.62247e10 0.966240
\(279\) −4.36228e10 −0.431017
\(280\) 1.49280e11 1.45141
\(281\) −1.45915e10 −0.139611 −0.0698057 0.997561i \(-0.522238\pi\)
−0.0698057 + 0.997561i \(0.522238\pi\)
\(282\) −1.70928e11 −1.60950
\(283\) −1.53399e10 −0.142162 −0.0710810 0.997471i \(-0.522645\pi\)
−0.0710810 + 0.997471i \(0.522645\pi\)
\(284\) 2.57386e11 2.34775
\(285\) 2.46668e10 0.221468
\(286\) −2.48224e11 −2.19380
\(287\) −7.52680e10 −0.654850
\(288\) 1.28706e10 0.110238
\(289\) 3.08013e11 2.59734
\(290\) −4.94519e11 −4.10575
\(291\) 8.30884e10 0.679238
\(292\) 1.55732e11 1.25359
\(293\) −9.22722e10 −0.731420 −0.365710 0.930729i \(-0.619174\pi\)
−0.365710 + 0.930729i \(0.619174\pi\)
\(294\) −8.13896e10 −0.635340
\(295\) −2.09761e10 −0.161259
\(296\) 1.86011e11 1.40840
\(297\) 3.02252e10 0.225406
\(298\) 1.52194e11 1.11796
\(299\) 1.56440e11 1.13195
\(300\) 9.04470e10 0.644687
\(301\) 8.88923e10 0.624187
\(302\) 4.15656e11 2.87543
\(303\) −1.42350e11 −0.970212
\(304\) −5.89434e10 −0.395826
\(305\) −2.37709e11 −1.57289
\(306\) −1.70450e11 −1.11135
\(307\) −8.99578e10 −0.577984 −0.288992 0.957331i \(-0.593320\pi\)
−0.288992 + 0.957331i \(0.593320\pi\)
\(308\) −2.36429e11 −1.49700
\(309\) −1.56549e11 −0.976872
\(310\) 4.57799e11 2.81544
\(311\) −1.16525e11 −0.706312 −0.353156 0.935564i \(-0.614891\pi\)
−0.353156 + 0.935564i \(0.614891\pi\)
\(312\) −1.97296e11 −1.17875
\(313\) 1.26016e11 0.742123 0.371061 0.928608i \(-0.378994\pi\)
0.371061 + 0.928608i \(0.378994\pi\)
\(314\) −3.74462e11 −2.17382
\(315\) 4.41217e10 0.252496
\(316\) −4.35717e11 −2.45817
\(317\) 1.70022e11 0.945665 0.472833 0.881152i \(-0.343232\pi\)
0.472833 + 0.881152i \(0.343232\pi\)
\(318\) −1.93100e11 −1.05891
\(319\) 4.08476e11 2.20855
\(320\) 1.61897e11 0.863107
\(321\) −3.97521e10 −0.208971
\(322\) 2.20300e11 1.14199
\(323\) 1.14901e11 0.587371
\(324\) 4.60638e10 0.232224
\(325\) −1.14500e11 −0.569285
\(326\) 2.80396e11 1.37497
\(327\) 1.35481e11 0.655258
\(328\) 4.30093e11 2.05178
\(329\) 2.06100e11 0.969833
\(330\) −3.17198e11 −1.47237
\(331\) −2.96557e11 −1.35795 −0.678973 0.734163i \(-0.737575\pi\)
−0.678973 + 0.734163i \(0.737575\pi\)
\(332\) 4.26590e11 1.92703
\(333\) 5.49782e10 0.245014
\(334\) −8.94173e10 −0.393154
\(335\) 4.16827e11 1.80823
\(336\) −1.05433e11 −0.451282
\(337\) −8.51827e10 −0.359763 −0.179882 0.983688i \(-0.557571\pi\)
−0.179882 + 0.983688i \(0.557571\pi\)
\(338\) 5.71018e10 0.237971
\(339\) −8.71517e10 −0.358408
\(340\) 1.20989e12 4.91011
\(341\) −3.78144e11 −1.51448
\(342\) −4.59090e10 −0.181460
\(343\) 2.54903e11 0.994377
\(344\) −5.07944e11 −1.95570
\(345\) 1.99910e11 0.759709
\(346\) −6.56814e10 −0.246377
\(347\) −2.47414e11 −0.916098 −0.458049 0.888927i \(-0.651452\pi\)
−0.458049 + 0.888927i \(0.651452\pi\)
\(348\) 6.22525e11 2.27536
\(349\) 2.31188e11 0.834163 0.417081 0.908869i \(-0.363053\pi\)
0.417081 + 0.908869i \(0.363053\pi\)
\(350\) −1.61240e11 −0.574336
\(351\) −5.83136e10 −0.205063
\(352\) 1.11568e11 0.387346
\(353\) 3.28570e11 1.12627 0.563134 0.826366i \(-0.309596\pi\)
0.563134 + 0.826366i \(0.309596\pi\)
\(354\) 3.90399e10 0.132128
\(355\) −4.16371e11 −1.39140
\(356\) −2.83029e9 −0.00933910
\(357\) 2.05524e11 0.669663
\(358\) 1.23876e11 0.398577
\(359\) −2.45562e11 −0.780253 −0.390126 0.920761i \(-0.627569\pi\)
−0.390126 + 0.920761i \(0.627569\pi\)
\(360\) −2.52118e11 −0.791121
\(361\) −2.91740e11 −0.904095
\(362\) −5.16049e11 −1.57944
\(363\) 7.10133e10 0.214664
\(364\) 4.56144e11 1.36190
\(365\) −2.51926e11 −0.742943
\(366\) 4.42416e11 1.28874
\(367\) −9.21749e10 −0.265226 −0.132613 0.991168i \(-0.542337\pi\)
−0.132613 + 0.991168i \(0.542337\pi\)
\(368\) −4.77700e11 −1.35781
\(369\) 1.27120e11 0.356940
\(370\) −5.76968e11 −1.60046
\(371\) 2.32836e11 0.638068
\(372\) −5.76299e11 −1.56029
\(373\) −7.33556e11 −1.96220 −0.981101 0.193499i \(-0.938016\pi\)
−0.981101 + 0.193499i \(0.938016\pi\)
\(374\) −1.47754e12 −3.90498
\(375\) 1.27546e11 0.333062
\(376\) −1.17769e12 −3.03868
\(377\) −7.88074e11 −2.00924
\(378\) −8.21178e10 −0.206883
\(379\) 1.43975e11 0.358434 0.179217 0.983810i \(-0.442644\pi\)
0.179217 + 0.983810i \(0.442644\pi\)
\(380\) 3.25873e11 0.801718
\(381\) 3.67023e11 0.892341
\(382\) 5.46136e11 1.31225
\(383\) −1.57608e11 −0.374269 −0.187135 0.982334i \(-0.559920\pi\)
−0.187135 + 0.982334i \(0.559920\pi\)
\(384\) −3.82672e11 −0.898124
\(385\) 3.82469e11 0.887204
\(386\) 1.43171e12 3.28255
\(387\) −1.50130e11 −0.340226
\(388\) 1.09768e12 2.45885
\(389\) 4.23390e11 0.937492 0.468746 0.883333i \(-0.344706\pi\)
0.468746 + 0.883333i \(0.344706\pi\)
\(390\) 6.11972e11 1.33949
\(391\) 9.31202e11 2.01488
\(392\) −5.60773e11 −1.19950
\(393\) 1.43244e11 0.302907
\(394\) −1.23762e12 −2.58735
\(395\) 7.04856e11 1.45685
\(396\) 3.99304e11 0.815972
\(397\) −3.97616e11 −0.803352 −0.401676 0.915782i \(-0.631572\pi\)
−0.401676 + 0.915782i \(0.631572\pi\)
\(398\) −1.05851e12 −2.11457
\(399\) 5.53560e10 0.109342
\(400\) 3.49633e11 0.682877
\(401\) −3.96502e11 −0.765766 −0.382883 0.923797i \(-0.625069\pi\)
−0.382883 + 0.923797i \(0.625069\pi\)
\(402\) −7.75783e11 −1.48157
\(403\) 7.29556e11 1.37780
\(404\) −1.88059e12 −3.51218
\(405\) −7.45171e10 −0.137628
\(406\) −1.10977e12 −2.02706
\(407\) 4.76579e11 0.860914
\(408\) −1.17440e12 −2.09819
\(409\) 5.75923e11 1.01768 0.508838 0.860862i \(-0.330075\pi\)
0.508838 + 0.860862i \(0.330075\pi\)
\(410\) −1.33406e12 −2.33156
\(411\) 4.55439e11 0.787304
\(412\) −2.06817e12 −3.53629
\(413\) −4.70733e10 −0.0796159
\(414\) −3.72064e11 −0.622467
\(415\) −6.90092e11 −1.14206
\(416\) −2.15250e11 −0.352389
\(417\) 1.95955e11 0.317354
\(418\) −3.97962e11 −0.637601
\(419\) −1.06755e12 −1.69210 −0.846048 0.533106i \(-0.821025\pi\)
−0.846048 + 0.533106i \(0.821025\pi\)
\(420\) 5.82891e11 0.914041
\(421\) 3.10696e11 0.482021 0.241011 0.970522i \(-0.422521\pi\)
0.241011 + 0.970522i \(0.422521\pi\)
\(422\) −8.59420e11 −1.31917
\(423\) −3.48082e11 −0.528628
\(424\) −1.33046e12 −1.99919
\(425\) −6.81555e11 −1.01333
\(426\) 7.74935e11 1.14004
\(427\) −5.33455e11 −0.776555
\(428\) −5.25163e11 −0.756480
\(429\) −5.05492e11 −0.720537
\(430\) 1.57554e12 2.22239
\(431\) 2.59339e11 0.362010 0.181005 0.983482i \(-0.442065\pi\)
0.181005 + 0.983482i \(0.442065\pi\)
\(432\) 1.78065e11 0.245981
\(433\) −9.45969e11 −1.29325 −0.646624 0.762809i \(-0.723820\pi\)
−0.646624 + 0.762809i \(0.723820\pi\)
\(434\) 1.02737e12 1.39002
\(435\) −1.00705e12 −1.34850
\(436\) 1.78983e12 2.37204
\(437\) 2.50810e11 0.328987
\(438\) 4.68876e11 0.608730
\(439\) −1.18489e12 −1.52261 −0.761306 0.648393i \(-0.775441\pi\)
−0.761306 + 0.648393i \(0.775441\pi\)
\(440\) −2.18549e12 −2.77978
\(441\) −1.65744e11 −0.208672
\(442\) 2.85063e12 3.55256
\(443\) −1.78010e11 −0.219597 −0.109799 0.993954i \(-0.535021\pi\)
−0.109799 + 0.993954i \(0.535021\pi\)
\(444\) 7.26316e11 0.886956
\(445\) 4.57853e9 0.00553485
\(446\) 7.43018e11 0.889185
\(447\) 3.09933e11 0.367184
\(448\) 3.63321e11 0.426127
\(449\) −2.46559e11 −0.286294 −0.143147 0.989701i \(-0.545722\pi\)
−0.143147 + 0.989701i \(0.545722\pi\)
\(450\) 2.72317e11 0.313054
\(451\) 1.10194e12 1.25419
\(452\) −1.15136e12 −1.29744
\(453\) 8.46454e11 0.944412
\(454\) 1.31168e12 1.44903
\(455\) −7.37900e11 −0.807136
\(456\) −3.16312e11 −0.342590
\(457\) 5.95044e10 0.0638155 0.0319077 0.999491i \(-0.489842\pi\)
0.0319077 + 0.999491i \(0.489842\pi\)
\(458\) −3.57343e11 −0.379482
\(459\) −3.47109e11 −0.365014
\(460\) 2.64100e12 2.75016
\(461\) −7.50852e11 −0.774284 −0.387142 0.922020i \(-0.626538\pi\)
−0.387142 + 0.922020i \(0.626538\pi\)
\(462\) −7.11838e11 −0.726930
\(463\) −3.64780e11 −0.368907 −0.184453 0.982841i \(-0.559051\pi\)
−0.184453 + 0.982841i \(0.559051\pi\)
\(464\) 2.40644e12 2.41015
\(465\) 9.32275e11 0.924710
\(466\) −5.41120e11 −0.531566
\(467\) −8.88180e11 −0.864122 −0.432061 0.901844i \(-0.642213\pi\)
−0.432061 + 0.901844i \(0.642213\pi\)
\(468\) −7.70380e11 −0.742333
\(469\) 9.35420e11 0.892748
\(470\) 3.65294e12 3.45305
\(471\) −7.62566e11 −0.713975
\(472\) 2.68984e11 0.249452
\(473\) −1.30140e12 −1.19546
\(474\) −1.31185e12 −1.19367
\(475\) −1.83570e11 −0.165455
\(476\) 2.71517e12 2.42419
\(477\) −3.93235e11 −0.347792
\(478\) 4.42316e11 0.387531
\(479\) 1.10248e12 0.956886 0.478443 0.878119i \(-0.341201\pi\)
0.478443 + 0.878119i \(0.341201\pi\)
\(480\) −2.75060e11 −0.236506
\(481\) −9.19466e11 −0.783219
\(482\) 1.40798e12 1.18819
\(483\) 4.48626e11 0.375079
\(484\) 9.38155e11 0.777089
\(485\) −1.77571e12 −1.45725
\(486\) 1.38689e11 0.112766
\(487\) −4.20755e11 −0.338960 −0.169480 0.985534i \(-0.554209\pi\)
−0.169480 + 0.985534i \(0.554209\pi\)
\(488\) 3.04824e12 2.43310
\(489\) 5.71006e11 0.451597
\(490\) 1.73940e12 1.36307
\(491\) −1.88333e12 −1.46238 −0.731188 0.682176i \(-0.761034\pi\)
−0.731188 + 0.682176i \(0.761034\pi\)
\(492\) 1.67938e12 1.29213
\(493\) −4.69098e12 −3.57645
\(494\) 7.67791e11 0.580058
\(495\) −6.45951e11 −0.483589
\(496\) −2.22775e12 −1.65272
\(497\) −9.34397e11 −0.686954
\(498\) 1.28437e12 0.935750
\(499\) −3.11715e11 −0.225064 −0.112532 0.993648i \(-0.535896\pi\)
−0.112532 + 0.993648i \(0.535896\pi\)
\(500\) 1.68500e12 1.20569
\(501\) −1.82092e11 −0.129128
\(502\) −4.55980e12 −3.20464
\(503\) 1.53038e12 1.06597 0.532984 0.846125i \(-0.321071\pi\)
0.532984 + 0.846125i \(0.321071\pi\)
\(504\) −5.65790e11 −0.390587
\(505\) 3.04221e12 2.08151
\(506\) −3.22524e12 −2.18718
\(507\) 1.16284e11 0.0781598
\(508\) 4.84873e12 3.23029
\(509\) −1.02987e12 −0.680069 −0.340035 0.940413i \(-0.610439\pi\)
−0.340035 + 0.940413i \(0.610439\pi\)
\(510\) 3.64273e12 2.38430
\(511\) −5.65360e11 −0.366801
\(512\) −3.15084e12 −2.02634
\(513\) −9.34905e10 −0.0595991
\(514\) 2.29754e12 1.45188
\(515\) 3.34566e12 2.09580
\(516\) −1.98336e12 −1.23162
\(517\) −3.01735e12 −1.85746
\(518\) −1.29480e12 −0.790168
\(519\) −1.33756e11 −0.0809206
\(520\) 4.21647e12 2.52891
\(521\) −1.97364e11 −0.117354 −0.0586770 0.998277i \(-0.518688\pi\)
−0.0586770 + 0.998277i \(0.518688\pi\)
\(522\) 1.87429e12 1.10489
\(523\) 2.24605e12 1.31269 0.656344 0.754462i \(-0.272102\pi\)
0.656344 + 0.754462i \(0.272102\pi\)
\(524\) 1.89239e12 1.09653
\(525\) −3.28354e11 −0.188636
\(526\) −1.05766e12 −0.602438
\(527\) 4.34265e12 2.45249
\(528\) 1.54355e12 0.864309
\(529\) 2.31510e11 0.128535
\(530\) 4.12680e12 2.27181
\(531\) 7.95020e10 0.0433963
\(532\) 7.31306e11 0.395819
\(533\) −2.12598e12 −1.14100
\(534\) −8.52140e9 −0.00453498
\(535\) 8.49553e11 0.448331
\(536\) −5.34513e12 −2.79716
\(537\) 2.52264e11 0.130909
\(538\) −1.41976e12 −0.730627
\(539\) −1.43675e12 −0.733218
\(540\) −9.84443e11 −0.498217
\(541\) 1.79418e12 0.900490 0.450245 0.892905i \(-0.351337\pi\)
0.450245 + 0.892905i \(0.351337\pi\)
\(542\) 3.69672e11 0.184001
\(543\) −1.05090e12 −0.518754
\(544\) −1.28126e12 −0.627254
\(545\) −2.89539e12 −1.40580
\(546\) 1.37335e12 0.661326
\(547\) 1.20032e12 0.573261 0.286631 0.958041i \(-0.407465\pi\)
0.286631 + 0.958041i \(0.407465\pi\)
\(548\) 6.01680e12 2.85005
\(549\) 9.00950e11 0.423278
\(550\) 2.36058e12 1.09999
\(551\) −1.26347e12 −0.583959
\(552\) −2.56352e12 −1.17520
\(553\) 1.58180e12 0.719264
\(554\) −2.04330e12 −0.921593
\(555\) −1.17496e12 −0.525658
\(556\) 2.58875e12 1.14883
\(557\) −1.07143e12 −0.471646 −0.235823 0.971796i \(-0.575779\pi\)
−0.235823 + 0.971796i \(0.575779\pi\)
\(558\) −1.73512e12 −0.757661
\(559\) 2.51080e12 1.08757
\(560\) 2.25323e12 0.968187
\(561\) −3.00892e12 −1.28256
\(562\) −5.80383e11 −0.245415
\(563\) −4.60836e12 −1.93312 −0.966559 0.256444i \(-0.917449\pi\)
−0.966559 + 0.256444i \(0.917449\pi\)
\(564\) −4.59850e12 −1.91364
\(565\) 1.86254e12 0.768933
\(566\) −6.10151e11 −0.249899
\(567\) −1.67227e11 −0.0679490
\(568\) 5.33928e12 2.15236
\(569\) −3.75584e12 −1.50211 −0.751055 0.660240i \(-0.770454\pi\)
−0.751055 + 0.660240i \(0.770454\pi\)
\(570\) 9.81135e11 0.389307
\(571\) 3.33077e12 1.31124 0.655620 0.755091i \(-0.272407\pi\)
0.655620 + 0.755091i \(0.272407\pi\)
\(572\) −6.67804e12 −2.60835
\(573\) 1.11217e12 0.430997
\(574\) −2.99382e12 −1.15112
\(575\) −1.48772e12 −0.567567
\(576\) −6.13612e11 −0.232270
\(577\) −2.06344e12 −0.774998 −0.387499 0.921870i \(-0.626661\pi\)
−0.387499 + 0.921870i \(0.626661\pi\)
\(578\) 1.22514e13 4.56573
\(579\) 2.91557e12 1.07813
\(580\) −1.33042e13 −4.88159
\(581\) −1.54867e12 −0.563853
\(582\) 3.30488e12 1.19399
\(583\) −3.40876e12 −1.22205
\(584\) 3.23055e12 1.14926
\(585\) 1.24624e12 0.439946
\(586\) −3.67017e12 −1.28572
\(587\) −1.53457e12 −0.533476 −0.266738 0.963769i \(-0.585946\pi\)
−0.266738 + 0.963769i \(0.585946\pi\)
\(588\) −2.18964e12 −0.755397
\(589\) 1.16965e12 0.400440
\(590\) −8.34332e11 −0.283469
\(591\) −2.52033e12 −0.849795
\(592\) 2.80765e12 0.939498
\(593\) −9.77682e11 −0.324677 −0.162338 0.986735i \(-0.551904\pi\)
−0.162338 + 0.986735i \(0.551904\pi\)
\(594\) 1.20222e12 0.396228
\(595\) −4.39232e12 −1.43670
\(596\) 4.09451e12 1.32921
\(597\) −2.15558e12 −0.694513
\(598\) 6.22248e12 1.98979
\(599\) 1.37554e11 0.0436569 0.0218284 0.999762i \(-0.493051\pi\)
0.0218284 + 0.999762i \(0.493051\pi\)
\(600\) 1.87626e12 0.591034
\(601\) 2.24306e12 0.701303 0.350652 0.936506i \(-0.385960\pi\)
0.350652 + 0.936506i \(0.385960\pi\)
\(602\) 3.53573e12 1.09722
\(603\) −1.57983e12 −0.486611
\(604\) 1.11825e13 3.41879
\(605\) −1.51765e12 −0.460544
\(606\) −5.66205e12 −1.70548
\(607\) −4.73786e11 −0.141655 −0.0708277 0.997489i \(-0.522564\pi\)
−0.0708277 + 0.997489i \(0.522564\pi\)
\(608\) −3.45096e11 −0.102417
\(609\) −2.25998e12 −0.665773
\(610\) −9.45501e12 −2.76489
\(611\) 5.82139e12 1.68982
\(612\) −4.58565e12 −1.32135
\(613\) −2.21574e12 −0.633793 −0.316896 0.948460i \(-0.602641\pi\)
−0.316896 + 0.948460i \(0.602641\pi\)
\(614\) −3.57811e12 −1.01601
\(615\) −2.71672e12 −0.765784
\(616\) −4.90455e12 −1.37242
\(617\) −2.79669e12 −0.776894 −0.388447 0.921471i \(-0.626988\pi\)
−0.388447 + 0.921471i \(0.626988\pi\)
\(618\) −6.22682e12 −1.71719
\(619\) 5.88609e12 1.61146 0.805729 0.592285i \(-0.201774\pi\)
0.805729 + 0.592285i \(0.201774\pi\)
\(620\) 1.23163e13 3.34747
\(621\) −7.57683e11 −0.204445
\(622\) −4.63483e12 −1.24159
\(623\) 1.02749e10 0.00273263
\(624\) −2.97799e12 −0.786307
\(625\) −4.76389e12 −1.24883
\(626\) 5.01234e12 1.30454
\(627\) −8.10423e11 −0.209415
\(628\) −1.00742e13 −2.58460
\(629\) −5.47308e12 −1.39413
\(630\) 1.75496e12 0.443849
\(631\) −1.73807e11 −0.0436451 −0.0218225 0.999762i \(-0.506947\pi\)
−0.0218225 + 0.999762i \(0.506947\pi\)
\(632\) −9.03864e12 −2.25360
\(633\) −1.75015e12 −0.433270
\(634\) 6.76269e12 1.66233
\(635\) −7.84376e12 −1.91444
\(636\) −5.19502e12 −1.25901
\(637\) 2.77194e12 0.667047
\(638\) 1.62473e13 3.88229
\(639\) 1.57810e12 0.374439
\(640\) 8.17819e12 1.92685
\(641\) 3.58625e12 0.839034 0.419517 0.907748i \(-0.362199\pi\)
0.419517 + 0.907748i \(0.362199\pi\)
\(642\) −1.58116e12 −0.367339
\(643\) −4.38236e12 −1.01102 −0.505509 0.862821i \(-0.668695\pi\)
−0.505509 + 0.862821i \(0.668695\pi\)
\(644\) 5.92679e12 1.35779
\(645\) 3.20847e12 0.729927
\(646\) 4.57024e12 1.03251
\(647\) 8.09880e11 0.181699 0.0908493 0.995865i \(-0.471042\pi\)
0.0908493 + 0.995865i \(0.471042\pi\)
\(648\) 9.55561e11 0.212898
\(649\) 6.89163e11 0.152483
\(650\) −4.55428e12 −1.00071
\(651\) 2.09216e12 0.456542
\(652\) 7.54355e12 1.63479
\(653\) −6.63384e12 −1.42776 −0.713880 0.700268i \(-0.753064\pi\)
−0.713880 + 0.700268i \(0.753064\pi\)
\(654\) 5.38880e12 1.15184
\(655\) −3.06131e12 −0.649862
\(656\) 6.49182e12 1.36867
\(657\) 9.54834e11 0.199933
\(658\) 8.19774e12 1.70482
\(659\) 6.81084e12 1.40675 0.703374 0.710820i \(-0.251676\pi\)
0.703374 + 0.710820i \(0.251676\pi\)
\(660\) −8.53364e12 −1.75060
\(661\) −7.93016e12 −1.61575 −0.807877 0.589351i \(-0.799383\pi\)
−0.807877 + 0.589351i \(0.799383\pi\)
\(662\) −1.17957e13 −2.38706
\(663\) 5.80512e12 1.16681
\(664\) 8.84932e12 1.76666
\(665\) −1.18303e12 −0.234584
\(666\) 2.18679e12 0.430697
\(667\) −1.02396e13 −2.00317
\(668\) −2.40561e12 −0.467446
\(669\) 1.51310e12 0.292046
\(670\) 1.65795e13 3.17859
\(671\) 7.80989e12 1.48728
\(672\) −6.17276e11 −0.116766
\(673\) 8.46361e11 0.159033 0.0795166 0.996834i \(-0.474662\pi\)
0.0795166 + 0.996834i \(0.474662\pi\)
\(674\) −3.38818e12 −0.632408
\(675\) 5.54555e11 0.102820
\(676\) 1.53622e12 0.282940
\(677\) 7.18796e12 1.31509 0.657546 0.753414i \(-0.271594\pi\)
0.657546 + 0.753414i \(0.271594\pi\)
\(678\) −3.46650e12 −0.630025
\(679\) −3.98494e12 −0.719462
\(680\) 2.50984e13 4.50148
\(681\) 2.67115e12 0.475923
\(682\) −1.50409e13 −2.66221
\(683\) 2.97182e12 0.522552 0.261276 0.965264i \(-0.415857\pi\)
0.261276 + 0.965264i \(0.415857\pi\)
\(684\) −1.23510e12 −0.215750
\(685\) −9.73333e12 −1.68909
\(686\) 1.01389e13 1.74796
\(687\) −7.27705e11 −0.124638
\(688\) −7.66690e12 −1.30458
\(689\) 6.57654e12 1.11176
\(690\) 7.95150e12 1.33545
\(691\) 1.95699e12 0.326541 0.163271 0.986581i \(-0.447796\pi\)
0.163271 + 0.986581i \(0.447796\pi\)
\(692\) −1.76704e12 −0.292934
\(693\) −1.44961e12 −0.238754
\(694\) −9.84102e12 −1.61036
\(695\) −4.18781e12 −0.680856
\(696\) 1.29138e13 2.08600
\(697\) −1.26548e13 −2.03099
\(698\) 9.19561e12 1.46633
\(699\) −1.10195e12 −0.174589
\(700\) −4.33787e12 −0.682865
\(701\) −1.67805e12 −0.262467 −0.131234 0.991351i \(-0.541894\pi\)
−0.131234 + 0.991351i \(0.541894\pi\)
\(702\) −2.31945e12 −0.360470
\(703\) −1.47412e12 −0.227633
\(704\) −5.31909e12 −0.816133
\(705\) 7.43896e12 1.13413
\(706\) 1.30690e13 1.97980
\(707\) 6.82716e12 1.02767
\(708\) 1.05030e12 0.157095
\(709\) −6.62647e12 −0.984860 −0.492430 0.870352i \(-0.663891\pi\)
−0.492430 + 0.870352i \(0.663891\pi\)
\(710\) −1.65613e13 −2.44587
\(711\) −2.67150e12 −0.392050
\(712\) −5.87123e10 −0.00856188
\(713\) 9.47929e12 1.37364
\(714\) 8.17483e12 1.17716
\(715\) 1.08030e13 1.54585
\(716\) 3.33265e12 0.473894
\(717\) 9.00746e11 0.127282
\(718\) −9.76733e12 −1.37156
\(719\) 2.94579e12 0.411076 0.205538 0.978649i \(-0.434106\pi\)
0.205538 + 0.978649i \(0.434106\pi\)
\(720\) −3.80547e12 −0.527730
\(721\) 7.50815e12 1.03472
\(722\) −1.16041e13 −1.58926
\(723\) 2.86726e12 0.390252
\(724\) −1.38834e13 −1.87790
\(725\) 7.49449e12 1.00744
\(726\) 2.82459e12 0.377347
\(727\) 2.39601e12 0.318114 0.159057 0.987269i \(-0.449155\pi\)
0.159057 + 0.987269i \(0.449155\pi\)
\(728\) 9.46238e12 1.24856
\(729\) 2.82430e11 0.0370370
\(730\) −1.00205e13 −1.30598
\(731\) 1.49454e13 1.93589
\(732\) 1.19024e13 1.53227
\(733\) 1.44611e13 1.85026 0.925130 0.379651i \(-0.123956\pi\)
0.925130 + 0.379651i \(0.123956\pi\)
\(734\) −3.66630e12 −0.466225
\(735\) 3.54217e12 0.447689
\(736\) −2.79679e12 −0.351326
\(737\) −1.36947e13 −1.70982
\(738\) 5.05626e12 0.627445
\(739\) 3.45079e12 0.425616 0.212808 0.977094i \(-0.431739\pi\)
0.212808 + 0.977094i \(0.431739\pi\)
\(740\) −1.55223e13 −1.90289
\(741\) 1.56355e12 0.190516
\(742\) 9.26114e12 1.12162
\(743\) −1.49532e13 −1.80005 −0.900025 0.435839i \(-0.856452\pi\)
−0.900025 + 0.435839i \(0.856452\pi\)
\(744\) −1.19549e13 −1.43044
\(745\) −6.62366e12 −0.787762
\(746\) −2.91775e13 −3.44924
\(747\) 2.61554e12 0.307340
\(748\) −3.97507e13 −4.64288
\(749\) 1.90652e12 0.221347
\(750\) 5.07320e12 0.585472
\(751\) −9.02826e12 −1.03568 −0.517839 0.855478i \(-0.673263\pi\)
−0.517839 + 0.855478i \(0.673263\pi\)
\(752\) −1.77760e13 −2.02700
\(753\) −9.28572e12 −1.05254
\(754\) −3.13460e13 −3.53193
\(755\) −1.80898e13 −2.02616
\(756\) −2.20923e12 −0.245976
\(757\) 5.66897e11 0.0627441 0.0313720 0.999508i \(-0.490012\pi\)
0.0313720 + 0.999508i \(0.490012\pi\)
\(758\) 5.72666e12 0.630072
\(759\) −6.56798e12 −0.718363
\(760\) 6.76000e12 0.734997
\(761\) 4.14422e12 0.447932 0.223966 0.974597i \(-0.428100\pi\)
0.223966 + 0.974597i \(0.428100\pi\)
\(762\) 1.45985e13 1.56860
\(763\) −6.49769e12 −0.694062
\(764\) 1.46928e13 1.56022
\(765\) 7.41817e12 0.783106
\(766\) −6.26894e12 −0.657907
\(767\) −1.32961e12 −0.138722
\(768\) −1.13423e13 −1.17646
\(769\) 1.43841e13 1.48325 0.741623 0.670817i \(-0.234056\pi\)
0.741623 + 0.670817i \(0.234056\pi\)
\(770\) 1.52129e13 1.55957
\(771\) 4.67879e12 0.476858
\(772\) 3.85175e13 3.90284
\(773\) −1.23525e13 −1.24436 −0.622180 0.782874i \(-0.713753\pi\)
−0.622180 + 0.782874i \(0.713753\pi\)
\(774\) −5.97149e12 −0.598065
\(775\) −6.93798e12 −0.690837
\(776\) 2.27706e13 2.25422
\(777\) −2.63677e12 −0.259524
\(778\) 1.68405e13 1.64796
\(779\) −3.40844e12 −0.331618
\(780\) 1.64640e13 1.59261
\(781\) 1.36798e13 1.31568
\(782\) 3.70390e13 3.54184
\(783\) 3.81687e12 0.362894
\(784\) −8.46431e12 −0.800146
\(785\) 1.62970e13 1.53177
\(786\) 5.69760e12 0.532464
\(787\) −9.90204e12 −0.920107 −0.460053 0.887891i \(-0.652170\pi\)
−0.460053 + 0.887891i \(0.652170\pi\)
\(788\) −3.32961e13 −3.07627
\(789\) −2.15386e12 −0.197866
\(790\) 2.80360e13 2.56091
\(791\) 4.17982e12 0.379633
\(792\) 8.28328e12 0.748065
\(793\) −1.50677e13 −1.35306
\(794\) −1.58153e13 −1.41217
\(795\) 8.40394e12 0.746158
\(796\) −2.84774e13 −2.51415
\(797\) −2.10226e13 −1.84554 −0.922769 0.385353i \(-0.874080\pi\)
−0.922769 + 0.385353i \(0.874080\pi\)
\(798\) 2.20181e12 0.192206
\(799\) 3.46516e13 3.00789
\(800\) 2.04700e12 0.176690
\(801\) −1.73532e10 −0.00148948
\(802\) −1.57711e13 −1.34610
\(803\) 8.27698e12 0.702509
\(804\) −2.08711e13 −1.76154
\(805\) −9.58772e12 −0.804700
\(806\) 2.90184e13 2.42196
\(807\) −2.89125e12 −0.239969
\(808\) −3.90114e13 −3.21989
\(809\) 9.92457e12 0.814598 0.407299 0.913295i \(-0.366471\pi\)
0.407299 + 0.913295i \(0.366471\pi\)
\(810\) −2.96395e12 −0.241929
\(811\) 2.08737e13 1.69436 0.847180 0.531306i \(-0.178299\pi\)
0.847180 + 0.531306i \(0.178299\pi\)
\(812\) −2.98565e13 −2.41011
\(813\) 7.52811e11 0.0604336
\(814\) 1.89562e13 1.51335
\(815\) −1.22031e13 −0.968863
\(816\) −1.77263e13 −1.39963
\(817\) 4.02541e12 0.316090
\(818\) 2.29076e13 1.78892
\(819\) 2.79674e12 0.217207
\(820\) −3.58905e13 −2.77215
\(821\) −5.79690e12 −0.445299 −0.222649 0.974899i \(-0.571471\pi\)
−0.222649 + 0.974899i \(0.571471\pi\)
\(822\) 1.81153e13 1.38396
\(823\) −5.11028e12 −0.388280 −0.194140 0.980974i \(-0.562192\pi\)
−0.194140 + 0.980974i \(0.562192\pi\)
\(824\) −4.29027e13 −3.24199
\(825\) 4.80716e12 0.361282
\(826\) −1.87236e12 −0.139952
\(827\) −1.38342e13 −1.02844 −0.514222 0.857657i \(-0.671919\pi\)
−0.514222 + 0.857657i \(0.671919\pi\)
\(828\) −1.00097e13 −0.740092
\(829\) 1.98846e13 1.46225 0.731125 0.682244i \(-0.238996\pi\)
0.731125 + 0.682244i \(0.238996\pi\)
\(830\) −2.74487e13 −2.00757
\(831\) −4.16105e12 −0.302690
\(832\) 1.02622e13 0.742478
\(833\) 1.64998e13 1.18735
\(834\) 7.79420e12 0.557859
\(835\) 3.89154e12 0.277034
\(836\) −1.07065e13 −0.758085
\(837\) −3.53345e12 −0.248848
\(838\) −4.24623e13 −2.97444
\(839\) −2.27812e12 −0.158726 −0.0793629 0.996846i \(-0.525289\pi\)
−0.0793629 + 0.996846i \(0.525289\pi\)
\(840\) 1.20917e13 0.837972
\(841\) 3.70756e13 2.55568
\(842\) 1.23581e13 0.847318
\(843\) −1.18191e12 −0.0806047
\(844\) −2.31212e13 −1.56844
\(845\) −2.48514e12 −0.167685
\(846\) −1.38451e13 −0.929246
\(847\) −3.40582e12 −0.227377
\(848\) −2.00819e13 −1.33359
\(849\) −1.24253e12 −0.0820772
\(850\) −2.71092e13 −1.78128
\(851\) −1.19469e13 −0.780855
\(852\) 2.08482e13 1.35547
\(853\) −7.01843e12 −0.453910 −0.226955 0.973905i \(-0.572877\pi\)
−0.226955 + 0.973905i \(0.572877\pi\)
\(854\) −2.12184e13 −1.36506
\(855\) 1.99801e12 0.127865
\(856\) −1.08941e13 −0.693523
\(857\) 2.61156e12 0.165381 0.0826905 0.996575i \(-0.473649\pi\)
0.0826905 + 0.996575i \(0.473649\pi\)
\(858\) −2.01062e13 −1.26659
\(859\) −1.25048e13 −0.783624 −0.391812 0.920045i \(-0.628152\pi\)
−0.391812 + 0.920045i \(0.628152\pi\)
\(860\) 4.23870e13 2.64235
\(861\) −6.09671e12 −0.378078
\(862\) 1.03153e13 0.636357
\(863\) −1.54530e13 −0.948338 −0.474169 0.880434i \(-0.657252\pi\)
−0.474169 + 0.880434i \(0.657252\pi\)
\(864\) 1.04252e12 0.0636459
\(865\) 2.85853e12 0.173608
\(866\) −3.76264e13 −2.27333
\(867\) 2.49491e13 1.49958
\(868\) 2.76395e13 1.65269
\(869\) −2.31579e13 −1.37756
\(870\) −4.00561e13 −2.37045
\(871\) 2.64213e13 1.55551
\(872\) 3.71288e13 2.17463
\(873\) 6.73016e12 0.392158
\(874\) 9.97610e12 0.578308
\(875\) −6.11714e12 −0.352787
\(876\) 1.26143e13 0.723759
\(877\) 3.17085e13 1.80999 0.904997 0.425417i \(-0.139873\pi\)
0.904997 + 0.425417i \(0.139873\pi\)
\(878\) −4.71297e13 −2.67651
\(879\) −7.47405e12 −0.422285
\(880\) −3.29877e13 −1.85430
\(881\) 2.45926e13 1.37535 0.687673 0.726020i \(-0.258632\pi\)
0.687673 + 0.726020i \(0.258632\pi\)
\(882\) −6.59256e12 −0.366814
\(883\) 1.49981e13 0.830257 0.415128 0.909763i \(-0.363737\pi\)
0.415128 + 0.909763i \(0.363737\pi\)
\(884\) 7.66913e13 4.22387
\(885\) −1.69906e12 −0.0931031
\(886\) −7.08043e12 −0.386018
\(887\) −1.14485e13 −0.620999 −0.310500 0.950574i \(-0.600496\pi\)
−0.310500 + 0.950574i \(0.600496\pi\)
\(888\) 1.50669e13 0.813141
\(889\) −1.76025e13 −0.945186
\(890\) 1.82113e11 0.00972941
\(891\) 2.44824e12 0.130138
\(892\) 1.99896e13 1.05721
\(893\) 9.33307e12 0.491126
\(894\) 1.23277e13 0.645452
\(895\) −5.39121e12 −0.280855
\(896\) 1.83531e13 0.951311
\(897\) 1.26716e13 0.653532
\(898\) −9.80700e12 −0.503260
\(899\) −4.77524e13 −2.43824
\(900\) 7.32621e12 0.372210
\(901\) 3.91465e13 1.97894
\(902\) 4.38302e13 2.20467
\(903\) 7.20028e12 0.360375
\(904\) −2.38841e13 −1.18946
\(905\) 2.24590e13 1.11294
\(906\) 3.36681e13 1.66013
\(907\) −1.35483e12 −0.0664740 −0.0332370 0.999447i \(-0.510582\pi\)
−0.0332370 + 0.999447i \(0.510582\pi\)
\(908\) 3.52885e13 1.72285
\(909\) −1.15304e13 −0.560152
\(910\) −2.93503e13 −1.41882
\(911\) −1.98115e13 −0.952984 −0.476492 0.879179i \(-0.658092\pi\)
−0.476492 + 0.879179i \(0.658092\pi\)
\(912\) −4.77442e12 −0.228530
\(913\) 2.26728e13 1.07991
\(914\) 2.36681e12 0.112178
\(915\) −1.92545e13 −0.908106
\(916\) −9.61369e12 −0.451191
\(917\) −6.87002e12 −0.320846
\(918\) −1.38064e13 −0.641637
\(919\) −3.57149e12 −0.165169 −0.0825847 0.996584i \(-0.526318\pi\)
−0.0825847 + 0.996584i \(0.526318\pi\)
\(920\) 5.47857e13 2.52128
\(921\) −7.28658e12 −0.333699
\(922\) −2.98655e13 −1.36107
\(923\) −2.63924e13 −1.19694
\(924\) −1.91507e13 −0.864295
\(925\) 8.74401e12 0.392711
\(926\) −1.45093e13 −0.648481
\(927\) −1.26805e13 −0.563997
\(928\) 1.40890e13 0.623611
\(929\) −3.50882e13 −1.54557 −0.772787 0.634665i \(-0.781138\pi\)
−0.772787 + 0.634665i \(0.781138\pi\)
\(930\) 3.70817e13 1.62550
\(931\) 4.44407e12 0.193869
\(932\) −1.45579e13 −0.632013
\(933\) −9.43850e12 −0.407789
\(934\) −3.53278e13 −1.51899
\(935\) 6.43044e13 2.75162
\(936\) −1.59810e13 −0.680553
\(937\) 3.73196e13 1.58164 0.790822 0.612047i \(-0.209653\pi\)
0.790822 + 0.612047i \(0.209653\pi\)
\(938\) 3.72068e13 1.56931
\(939\) 1.02073e13 0.428465
\(940\) 9.82759e13 4.10555
\(941\) −6.95147e12 −0.289017 −0.144508 0.989504i \(-0.546160\pi\)
−0.144508 + 0.989504i \(0.546160\pi\)
\(942\) −3.03314e13 −1.25506
\(943\) −2.76233e13 −1.13756
\(944\) 4.06004e12 0.166401
\(945\) 3.57386e12 0.145779
\(946\) −5.17638e13 −2.10144
\(947\) 1.32678e12 0.0536071 0.0268036 0.999641i \(-0.491467\pi\)
0.0268036 + 0.999641i \(0.491467\pi\)
\(948\) −3.52931e13 −1.41923
\(949\) −1.59688e13 −0.639109
\(950\) −7.30159e12 −0.290845
\(951\) 1.37718e13 0.545980
\(952\) 5.63244e13 2.22244
\(953\) −6.00433e12 −0.235802 −0.117901 0.993025i \(-0.537616\pi\)
−0.117901 + 0.993025i \(0.537616\pi\)
\(954\) −1.56411e13 −0.611364
\(955\) −2.37685e13 −0.924668
\(956\) 1.18997e13 0.460762
\(957\) 3.30865e13 1.27511
\(958\) 4.38516e13 1.68206
\(959\) −2.18430e13 −0.833929
\(960\) 1.31137e13 0.498315
\(961\) 1.77669e13 0.671981
\(962\) −3.65722e13 −1.37678
\(963\) −3.21992e12 −0.120650
\(964\) 3.78793e13 1.41272
\(965\) −6.23095e13 −2.31303
\(966\) 1.78443e13 0.659330
\(967\) −7.02355e12 −0.258308 −0.129154 0.991625i \(-0.541226\pi\)
−0.129154 + 0.991625i \(0.541226\pi\)
\(968\) 1.94614e13 0.712417
\(969\) 9.30698e12 0.339119
\(970\) −7.06295e13 −2.56161
\(971\) 1.65621e13 0.597900 0.298950 0.954269i \(-0.403364\pi\)
0.298950 + 0.954269i \(0.403364\pi\)
\(972\) 3.73117e12 0.134075
\(973\) −9.39806e12 −0.336148
\(974\) −1.67357e13 −0.595840
\(975\) −9.27448e12 −0.328677
\(976\) 4.60101e13 1.62304
\(977\) −3.57670e12 −0.125591 −0.0627953 0.998026i \(-0.520002\pi\)
−0.0627953 + 0.998026i \(0.520002\pi\)
\(978\) 2.27120e13 0.793837
\(979\) −1.50427e11 −0.00523362
\(980\) 4.67955e13 1.62064
\(981\) 1.09739e13 0.378313
\(982\) −7.49102e13 −2.57063
\(983\) −3.08375e13 −1.05339 −0.526695 0.850054i \(-0.676569\pi\)
−0.526695 + 0.850054i \(0.676569\pi\)
\(984\) 3.48375e13 1.18459
\(985\) 5.38628e13 1.82316
\(986\) −1.86586e14 −6.28684
\(987\) 1.66941e13 0.559934
\(988\) 2.06561e13 0.689670
\(989\) 3.26234e13 1.08429
\(990\) −2.56930e13 −0.850074
\(991\) 5.24418e12 0.172721 0.0863607 0.996264i \(-0.472476\pi\)
0.0863607 + 0.996264i \(0.472476\pi\)
\(992\) −1.30428e13 −0.427630
\(993\) −2.40211e13 −0.784010
\(994\) −3.71661e13 −1.20756
\(995\) 4.60676e13 1.49002
\(996\) 3.45538e13 1.11257
\(997\) −3.58536e13 −1.14922 −0.574611 0.818427i \(-0.694847\pi\)
−0.574611 + 0.818427i \(0.694847\pi\)
\(998\) −1.23986e13 −0.395627
\(999\) 4.45324e12 0.141459
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 177.10.a.a.1.21 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.a.1.21 21 1.1 even 1 trivial